Character rig not moving certain parts of mesh (Meta-Rig)
Yes, it's a weight problem: having the pad with the correct weight relatively to the arm bone is not enough: you have to remove its weights relatively to others bones (chest, head, shoulders).
Check theese answers for more infos:
How to make &quot;Weight Paint&quot; affect all vertices, even those with zero weight?
Add armor to the body without long weight paint